The objective of this study was to evaluate the accuracy of various sensor fusion algorithms for measuring upper arm elevation relative to gravity (i.e., angular displacement and velocity summary measures) across different motion speeds. Thirteen participants completed a cyclic, short duration, arm-intensive work task that involved transfering wooden dowels at three work rates (slow, medium, fast). Angular displacement and velocity measurements of upper arm elevation were simultaneously measured using an inertial measurement unit (IMU) and an optical motion capture (OMC) system. Results indicated that IMU-based inclinometer solutions can reduce root-mean-square errors in comparison to accelerometer-based inclination estimates by as much as 87%, depending on the work rate and sensor fusion approach applied. The findings suggest that IMU-based inclinometers can substantially improve inclinometer accuracy in comparison to traditional accelerometer-based inclinometers. Ergonomists may use the non-proprietary sensor fusion algorithms provided here to more accurately estimate upper arm elevation.

Measuring human motion with accuracy is critical for many applications in occupational ergonomics, such as estimating exposure to non-neutral working postures (

Dual-axis and tri-axial piezoresistive accelerometers are commonly used as inclinometers in field-based applications to estimate posture and movements of the trunk and upper arm with respect to the gravity vector (

Previous research suggests that IMU-based motion capture can be highly accurate in controlled, laboratory settings (

Few studies that have evaluated IMU-based inclinometers, however, have also reported the accuracy of (i) accelerometer-derived angular displacement measurements, (ii) angular velocity measurements, or (iii) posture and movement summary measures used for health-based decision making in the context of occupational ergonomics. Thus, the ability of IMU-based inclinometers to improve measurement accuracy relative to established accelerometer-based approaches remains unclear. Previous work compared accelerometer and IMU-based inclinometers to an electrogoniometer used to measure trunk motion (

Acknowledging that field-based IMU measurement of full three-dimensional motion may not be achievable in many industrial environments due to magnetic field disturbances, we explored the potential benefits of intermediary solutions (IMU-based inclinometers) that forgo the use of magnetometer data and instead rely on accelerometer and gyroscope data. The specific objective of this laboratory study was to evaluate the effects of motion speed and upper arm elevation calculation method (i.e., no sensor fusion and a variety of sensor fusion approaches) on the error in measures of upper arm posture and movement. In particular, we aimed to isolate the error associated with the sensor (i.e., technological error) (

Thirteen participants (11 male, mean age 27.2 ± 6.6 years, right-hand dominant) were recruited from the University of Iowa community. All participants were screened for any self-reported cases of: (i) physician-diagnosed musculoskeletal disorder in the past six months, (ii) pain during the previous two weeks prior to enrollment, and (iii) medical history of orthopedic surgery in the upper extremity (shoulder, elbow, wrist, hand). Each participant provided written informed consent. The University of Iowa Institutional Review Board approved all study procedures.

Each participant completed six trials of a simulated work task that involved transferring wooden dowels (2 cm diameter x 8 cm length) from a waist-high container in front of the participant to a shoulder-height container located 45° diagonally from the participant (

An IMU (series SXT, Nexgen Ergonomics, Inc., Pointe Claire, Quebec, CA) was secured to the lateral aspect of the dominant upper arm midway between the acromion and the lateral epicondyle (

Spatial orientation was also simultaneously recorded using a six-camera OMC system (Optitrack Flex 13, NaturalPoint, Inc., Corvallis, OR, USA) that tracked a cluster of four reflective markers mounted to the surface of the IMU with double-sided tape (

The spatial orientation derived from the OMC marker cluster was calculated using the quaternion output of the OMC system software. All post-processing was accomplished using MATLAB (2016a, Mathworks, Natick, MA). Data from both the IMU and OMC systems were recorded using the maximum available sampling rates. Therefore, the raw IMU data (128 Hz sampling rate) were down-sampled to 120 Hz (the OMC sampling rate) to maintain sample-to-sample temporal synchronization.

IMU inclination angles in the pitch (

The upper arm elevation displacement (

Pitch

The raw accelerometer data stream was low-pass filtered (2nd order Butterworth, 3 Hz corner frequency) prior to the angle calculations. Pitch and roll angles calculated without sensor fusion are described using the designation “Accel”.

IMU pitch

The design of the second-order complementary filter was a direct implementation of the filter developed by

The Extended Kalman filter used in this study was designed to discriminate the direction of gravity (^{b}) from the linear acceleration (^{b}) in the local coordinate frame when gyroscope measurements

Here, 0_{3×3} is a 3 × 3 matrix with zeros, _{3×3} is a 3 × 3 identity matrix, _{a}, _{b} are the parameters of the first-order Gauss-Markov process used to account for external acceleration. The gyroscope white noise, ^{ω}, gyroscope bias, ^{a}, are each assumed to follow a normal distribution of ^{gm}, is assumed to be zero mean with an identity covariance matrix. The assigned filter parameters are shown in ^{b} using (

The derivation and implementation of (

The offset between the local coordinate frames of the OMC and the IMU was calculated using angular rate measurements according to de Vries et al. (2010). After applying the local offset, the offset between the global coordinate frames of the OMC and the IMU was determined under static conditions using Accel-derived inclination measurements. OMC-derived upper arm elevation displacements and velocities were calculated after the offsets were added to OMC-derived orientation measurements.

Root-mean-square error (RMS) was calculated using (

A two-factor repeated measures analysis of variance (ANOVA) was used test the main and interactive effects of material transfer rate and upper arm elevation calculation method (i.e., Accel, Comp-1, Comp-2, Accel-KF, and Em-KF) on (i) RMS displacement error, (ii) peak displacement error, (iii) RMS velocity error, and (iv) peak velocity error. Pre-planned pairwise comparisons using Bonferroni corrections were used to test, at each level of motion speed, differences between RMS and peak errors (both for displacements and velocities) between (i) Accel and Comp-1, (ii) Accel and Comp-2, (iii) Accel and Accel-KF, and (iv) Accel and Em-KF. All statistical analyses were performed using SPSS (version 24, IBM Corporation, Armonk, NY).

The cyclic motion pattern and the changes to movement frequency associated with increased transfer rates (15, 30, 45 cycles/min) can be observed through the OMC-derived angular displacement measurements (

Although statistically significant pairwise comparisons were observed for the RMS and peak error measurements associated with the slowest transfer rate, the measurement errors were small (2.3° RMS, 6.8° peak for all calculation methods). Under the fastest transfer rate (maximum expected error), the errors associated with accelerometer-derived displacements were more apparent (11.3° RMS, 28.9° peak). The simple first-order complementary filter (Comp-1) reduced RMS error to 3.2°, while the Kalman filters reduced the RMS error to <1.5°. Similarly, a first-order complementary filter reduced peak error to 6.5°, while the Kalman filters reduced peak error to <3.2°. In general, the accelerometer-derived displacements underestimated upper arm elevation as transfer rates increased, as evidenced by the 90^{th} percentile measurements. This was mitigated by implementing a sensor fusion algorithm. Time-dependent errors were not observed for displacements calculated using sensor fusion algorithms (

The increase in amplitude and frequency of OMC-derived angular velocities associated with increased material transfer rates can be observed in

Unlike the accelerometer-derived displacements, the RMS and peak angular velocity error associated with accelerometer-derived angular velocities were more noticeable (13.0°/s RMS and 42.7°/s peak). RMS and peak velocity error for accelerometer-derived measurements increased to 81.7°/s and 221.3°/s for the fastest motion condition. The first-order complementary filter reduced RMS error to 17°/s, while the Kalman filters decreased RMS error to ≤9.3°/s. Similarly, the first-order complementary filter reduced peak error to 46.2°/s, while the Kalman filters reduced peak error to ≤25.2°/s (

The accelerometer-derived displacements were accurate (<2.5° RMS error, <7° peak error) for the slowest material transfer rates (15 cycles/min). This test condition corresponded to an acceleration average and standard deviation of 9.9 m/s^{2} and 0.4 m/s^{2} within each trial, respectively. The accelerometer-derived displacements were negatively affected by increased motion speeds. Under the fast motion condition, the RMS and peak displacement error increased to 11.3° and 28.9°, respectively. This observation was consistent with the expected increase in tangential and centripetal acceleration, which are both affected by increased angular velocities (

As expected, the sensor fusion algorithms improved measurement accuracy for upper arm elevation displacement. For every transfer rate tested, a statistically significant pairwise difference was observed between the accuracy of accelerometer-derived displacements and each of the sensor fusion algorithms. However, the improvements in measurement accuracy were more apparent with increased motion speeds. For the fast motion condition, a simple first-order complementary filter reduced the RMS displacement error from 11.3° to 3.2°. However, this filter design did not account for variability in gyroscope bias or non-gravitational acceleration. The Comp-2 filter, which reduced the RMS displacement error to <2.8°, accounted for gyroscope bias variability in the filter design. The modified linear Kalman filter accounted for both non-gravitational acceleration as well as gyroscope bias variability, which further reduced the error to <1.5°. In general, our errors were consistent with other studies (<4° RMS error) that provided inclination estimates using an identical comp-2 filter (

Similar error trends appeared in velocity measurements since velocity was calculated by taking the derivative of the angular displacements with respect to time. As expected, accelerometer-derived angular velocities were unusable for the fast motion conditions (81.7°/s RMS error). This was mitigated considerably using a sensor fusion algorithm, which resulted in RMS errors between 7.3°/s and 17.0°/s for the fastest transfer rate, depending on the sensor fusion algorithm. Few studies have published accuracy of angular velocity measurements. In general, our results are consistent with previous studies. For the accelerometer-derived angular velocities,

The relatively short sampling duration limits the extent to which the observed results can be applied to workplace exposure assessment practices. However, given the simplistic and cyclic motion (which was highly repeatable, as demonstrated in

A cyclic task was chosen to provide the maximum influence of motion on error magnitudes. However, the nature of the cyclic task precludes rest/recovery metrics that are also used to quantify motion-related exposures (e.g., the percentage of time with neutral posture and low velocity [

In general, the findings of this study suggest that the dynamics associated with upper arm motion are more than capable of adversely affecting accelerometer-derived angular displacement and velocity measurements commonly reported in the occupational ergonomics literature. Importantly, we observed underestimation of the extreme upper arm postures and velocities (i.e., 90^{th} percentiles) at increased motion speeds. This result has meaningful implications for both researchers and practitioners when considering the use of accelerometers to identify and mitigate work activities that impose the greatest biomechanical loading. Moreover, in epidemiologic studies, underestimation of upper arm elevation during fast motion speeds may impact observed associations between summary measures of exposure to non-neutral posture and musculoskeletal health outcomes. If fast motion speeds are experienced randomly among those with and without outcomes, then any underestimation of upper arm elevation would lead to an attenuation of risk estimates. On the other hand, if those experiencing outcomes are more likely engaged in work with fast motion speeds in comparison to those not experiencing outcomes (or

The overall goal of this study was to evaluate the capability of IMU-based inclinometers to provide accurate measurements of upper arm elevation displacement and velocity. In general, the accelerometer-derived displacements were accurate (<2.5° RMS error, <7° peak error) for slow movement speeds. However, both accelerometer-derived displacements and velocities were negatively affected by increased motion speeds. Under the fast motion speeds, the RMS and peak displacement errors increased to 11.3° and 28.9°, respectively. More importantly, the RMS and peak errors associated with accelerometer-derived velocities were substantial (81.7°/s and 221.3°/s, respectively). A Kalman filter reduced peak displacement and velocity errors to <3.5° and <25.1°/s, respectively across all testing conditions. The results indicate that IMU-based inclinometers, in particular when implemented using a Kalman filter, can substantially improve inclinometer accuracy for the assessment of upper arm elevation during fast motion speeds.

The first-order complementary filter contains the following structure (

The final equation of the first-order complementary filter (

The Extended Kalman Filter used in this study contains the generic process model (_{k}, a column vector containing the parameters of interest, from prior estimate _{k}, respectively. The measurement model compares _{k} to sensor measurements _{k}, where G is a matrix that relates _{k} to _{k}, and _{k} is the random variation within the measurement model. The random parameters _{k-1} and _{k} are assumed to follow normal distributions of

The implementation of the Kalman filter consists of a series of five recursive equations:
_{k}_{k} is the Kalman gain calculated from Q and R. Matrices A, W, H, and V are all Jacobin matrices. Matrix A contains the partial derivatives of

The Kalman Filter implemented was modified from a validated Linear Kalman Filter (^{b}) from the linear acceleration (^{b}) in the local coordinate frame when gyroscope measurements _{3×3} is a 3 × 3 matrix with zeros, _{3×3} is a 3 × 3 identity matrix, _{a}_{b} are the parameters of the first-order Gauss-Markov process used to account for external acceleration. The gyroscope noise ^{ω} and accelerometer noise v^{a} are assumed to follow a normal distribution of ^{gm} is assumed to be zero mean with an identity covariance matrix.

This process model was modified into a first-order approximation (

Based on these changes, (

Given that F is non-linear, A is defined as follows:

The process covariance matrix (Q) and the measurement covariance matrix (R) is defined as follows:

The MATLAB files for the filters in this paper are freely available using the following address:

Placement of the waist-height container holding the wooden dowels and the shoulder-height container.

IMU and its associated marker cluster attached to the upper arm of a participant.

OMC-derived upper arm elevation displacements (°) for one participant across three different material transfer rates: slow (15 cycles/min), medium (30 cycles/min), and fast (45 cycles/min).

Upper arm elevation displacements across two cycles at two material transfer rates: slow (15 cycles/min), and fast (45 cycles/min). Displacements were measured by the optical motion capture system (OMC) and calculated using an accelerometer (Accel), first-order complementary filter (Comp-1), and a modified linear Kalman filter (Accel-KF).

Sample-to-sample displacement difference between OMC and IMU using a modified linear Kalman filter across two material transfer rates: slow (15 cycles/min) and fast (45 cycles/min).

OMC-derived upper arm elevation velocities (one participant) across three material transfer rates: slow (15 cycles/min), medium (30 cycles/min), and fast (45 cycles/min).

Upper arm elevation velocities (°/s) for one participant across two material transfer rates: slow (15 cycles/min), and fast (45 cycles/min). Angular velocities were derived using displacements measured from the optical motion capture (OMC) calculated using an accelerometer (Accel), first-order complementary filter (Comp-1), and a modified linear Kalman filter (Accel-KF).

Kalman filter parameters.

Gyro White Noise | Gyro Bias | Accel White Noise | c_{a} | c_{b} | |
---|---|---|---|---|---|

| |||||

Accel-KF | 0.005 rad/s | 0.0005 (rad/s^{2}) | 0.005 m/s^{2} | 0.001 | 0.1 |

Mean(SD) within-trial acceleration measurements across all 13 participants and material transfer rates.

Slow (15 cycles/min) | Medium (30 cycles/min) | Fast (45 cycles/min) | |
---|---|---|---|

| |||

Average (m/s^{2}) | 9.9(0.3) | 10.1(0.3) | 10.4(0.2) |

Standard Deviation (m/s^{2}) | 0.4(0.1) | 1.0(0.2) | 1.5(0.2) |

Mean (SD) upper arm elevation displacement across 13 participants and three material transfer rates: slow (15 cycles/min), medium (30 cycles/min), and fast (45 cycles/min) that was maintained for a period of 1 min. Displacements were measured by the optical motion capture system (OMC) and calculated using an accelerometer (Accel), first-order complementary filter (Comp-1), a second-order complementary filter (Comp-2), a modified linear Kalman filter (Accel-KF), and an embedded Kalman filter (Em-KF).

Upper Arm Elevation Displacement | OMC | Accel | Comp-1 | Comp-2 | Accel-KF | Em-KF |
---|---|---|---|---|---|---|

| ||||||

| ||||||

RMS error (°) | -REF- | 2.3(0.4) | 1.6(0.9) | 1.8(0.5) | 1.1(0.6) | 1.2(0.9) |

Peak error (°) | -REF- | 6.8(1.7) | 3.3(1.4) | 4.1(1.0) | 2.2(1.0) | 2.4(1.6) |

Mean (°) | 47.4(7.7) | 46.5(7.8) | 46.9(8.2) | 46.6(7.9) | 46.7(7.8) | 46.8(7.4) |

10th Percentile (°) | 20.5(6.4) | 20.4(6.4) | 21.0(6.9) | 20.5(6.5) | 20.4(6.6) | 20.4(6.3) |

50th Percentile (°) | 46.1(8.9) | 46.2(8.7) | 45.5(9.2) | 45.9(8.8) | 45.4(8.8) | 45.5(8.5) |

90th Percentile (°) | 75.4(8.7) | 72.5(9.1) | 74.2(9.2) | 73.4(9.1) | 74.2(8.8) | 74.3(8.4) |

Percentile Range (90th – 10th)(°) | 54.9(4.4) | 52.1(4.5) | 53.2(4.1) | 52.9(4.3) | 53.7(4.0) | 53.9(4.0) |

Time in neutral posture (<20°) (%) | 12.3(13.7) | 12.0(12.9) | 11.6(13.9) | 12.2(13.4) | 12.3(13.7) | 12.1(13.2) |

Time in extreme posture (≥45°)(%) | 50.4(7.5) | 50.6(8.3) | 49.8(8.2) | 50.2(8.1) | 49.7(7.7) | 49.9(7.2) |

Time in extreme posture (≥60°)(%) | 35.4(12.4) | 33.4(13.7) | 34.0(13.4) | 33.8(13.4) | 34.0(13.2) | 34.7(11.8) |

| ||||||

RMS error (°) | -REF- | 6.3(1.5) | 2.4(1.0) | 2.4(0.6) | 1.3(0.6) | 1.4(1.0) |

Peak error (°) | -REF- | 17.5(4.6) | 5.7(4.4) | 5.3(1.2) | 2.7(1.1) | 2.5(1.5) |

Mean (°) | 44.4(7.3) | 42.9(7.4) | 43.8(7.6) | 44.2(7.8) | 43.7(7.4) | 43.5(7.5) |

10th Percentile (°) | 19.0(6.8) | 20.8(6.9) | 19.8(7.0) | 20.1(7.3) | 19.1(6.9) | 18.9(6.8) |

50th Percentile (°) | 41.8(8.1) | 43.9(7.6) | 41.1(8.1) | 41.5(8.2) | 41.1(8.0) | 40.9(8.2) |

90th Percentile (°) | 73.1(9.1) | 63.3(8.6) | 71.4(9.1) | 71.8(9.4) | 71.7(9.0) | 71.5(9.2) |

Percentile Range (90th – 10th)(°) | 54.1(5.4) | 42.5(4.7) | 51.6(5.2) | 51.7(5.0) | 52.7(5.3) | 52.7(5.2) |

Time in neutral posture (<20) (%) | 15.4(13.4) | 11.7(11.9) | 13.9(13.6) | 13.6(13.9) | 15.2(13.6) | 15.5(13.7) |

Time in extreme posture (≥45°)(%) | 46.3(8.5) | 46.9(12.3) | 45.4(9.0) | 45.8(9.1) | 45.5(8.7) | 45.2(8.8) |

Time in extreme posture (≥60°)(%) | 29.8(12.0) | 21.0(15.8) | 27.7(12.9) | 28.0(13.0) | 28.0(12.9) | 27.6(13.2) |

| ||||||

RMS error (°) | -REF- | 11.3(1.9) | 3.2(0.8) | 2.9(1.1) | 1.5(0.5) | 1.2(0.8) |

Peak error (°) | -REF- | 28.9(5.2) | 6.5(1.8) | 5.7(1.6) | 3.2(1.0) | 2.4(1.2) |

Mean (°) | 43.6(7.2) | 40.7(6.9) | 43.3(7.4) | 44.1(8.4) | 42.9(7.3) | 43.3(7.4) |

10th Percentile (°) | 18.1(5.8) | 23.0(6.4) | 19.5(6.3) | 19.4(6.9) | 18.2(6.0) | 18.5(5.9) |

50th Percentile (°) | 42.3(7.9) | 43.7(7.2) | 42.0(7.9) | 42.4(8.9) | 41.6(7.9) | 42.0(8.2) |

90th Percentile (°) | 71.1(9.1) | 54.8(7.8) | 69.2(9.2) | 71.3(10.2) | 69.8(9.2) | 70.2(9.1) |

Percentile Range (90th – 10th)(°) | 53.0(6.2) | 31.8(4.3) | 49.7(6.1) | 51.9(6.2) | 51.6(6.1) | 51.7(5.9) |

Time in neutral posture (<20) (%) | 16.1(11.4) | 8.0(9.6) | 12.9(12.2) | 14.2(13.3) | 15.9(11.8) | 15.5(12) |

Time in extreme posture (≥45°)(%) | 46.3(9.1) | 41.1(20.9) | 45.7(9.7) | 46.5(10.3) | 45.4(9.3) | 45.9(9.5) |

Time in extreme posture (≥60°)(%) | 28.1(12.8) | 8.3(10.2) | 25.5(14.3) | 27.7(14.6) | 25.9(13.9) | 26.7(13.9) |

Statistically-significant (

Statistically-significant (

Angular velocities of upper arm elevation across 13 participants and three material transfer rates: slow (15 cycles/min), medium (30 cycles/min), and fast (30 cycles/min) that was maintained for a period of 1 min. Angular velocities were calculated using displacement measurements obtained from an optical motion capture system (OMC) an accelerometer (Accel), first-order complementary filter (Comp-1), a modified linear Kalman filter (Accel-KF), and an embedded Kalman filter (Em-KF).

Velocity | OMC | Accel | Comp-1 | Comp-2 | Accel-KF | Em-KF |
---|---|---|---|---|---|---|

| ||||||

| ||||||

RMS error (°/s) | -REF- | 13.0(3.0) | 4.4(1.1) | 9.9(0.8) | 3.1(0.9) | 2.8(1.0) |

Peak error (°/s) | -REF- | 42.7(11.4) | 14.1(4.4) | 19.9(2.1) | 9.7(3.4) | 8.7(3.3) |

Mean (°/s) | 28.2(2.1) | 28.6(2.3) | 27.5(2.1) | 28.7(2.4) | 27.6(2.0) | 27.7(2.0) |

10th Percentile (°/s) | 2.6(1.1) | 4.0(1.3) | 2.9(1.3) | 4.4(0.7) | 2.7(1.2) | 2.6(1.2) |

50th Percentile (°/s) | 22.8(3.8) | 25.9(2.7) | 22.4(3.3) | 23.8(2.0) | 22.4(3.4) | 22.5(3.5) |

90th Percentile (°/s) | 61.3(8.7) | 56.6(7.0) | 59.4(8.4) | 59.6(7.7) | 59.9(8.4) | 60.1(8.5) |

Percentile Range (90th – 10th)(°/s) | 58.7(9.5) | 52.6(7.7) | 56.5(9.3) | 55.2(7.8) | 57.2(9.3) | 57.4(9.4) |

Time at low velocities (<5°/s)(%) | 19.5(6.4) | 13.2(3.7) | 18.1(6.2) | 11.5(1.9) | 19.0(6.3) | 19.6(6.3) |

Time at high velocities (≥90°/s)(%) | 1.0(1.5) | 0.4(0.6) | 0.8(1.3) | 0.8(1.2) | 0.9(1.4) | 0.8(1.4) |

| ||||||

RMS error (°/s) | -REF- | 39.8(10.9) | 10.3(2.4) | 11.1(1.4) | 5.9(1.4) | 5.1(2.0) |

Peak error (°/s) | -REF- | 112.5(29.1) | 30.8(10.0) | 25.6(7.9) | 17.1(4.3) | 15.3(7.7) |

Mean (°/s) | 56.0(5.3) | 49.7(5.9) | 54(5.4) | 54.3(5.3) | 54.8(5.3) | 54.7(5.2) |

10th Percentile (°/s) | 7.5(2.8) | 9.8(3.0) | 7.8(2.9) | 8.1(2.3) | 7.8(2.8) | 7.3(2.8) |

50th Percentile (°/s) | 52.6(6.1) | 49.3(7.2) | 50.0(5.5) | 49.9(6.2) | 51.3(5.8) | 51.4(6.0) |

90th Percentile (°/s) | 109.7(17.3) | 89.0(11.2) | 106.4(16.4) | 107.3(15.9) | 107.4(16.8) | 107.3(16.7) |

Percentile Range (90th – 10th)(°/s) | 102.2(19.0) | 79.2(10.7) | 98.6(17.7) | 99.2(17.0) | 99.6(18.4) | 99.9(18.3) |

Time at low velocities (<5°/s)(%) | 7.9(3.8) | 5.7(2.0) | 7.5(3.6) | 6.7(2.0) | 7.6(3.7) | 8.0(3.7) |

Time at high velocities (≥90°/s)(%) | 21.7(8.5) | 9.8(6.0) | 19(8.6) | 19.5(8.1) | 20.0(8.7) | 20.2(8.7) |

| ||||||

RMS error (°/s) | -REF- | 79.0(14.1) | 17.0(2.7) | 13.8(3.7) | 9.3(1.7) | 7.3(3.9) |

Peak error (°/s) | -REF- | 206.5(41.1) | 46.2(8.4) | 36.2(18.6) | 25.2(5.8) | 21.4(13.8) |

Mean (°/s) | 83.3(9.8) | 62.5(7.2) | 78.8(9.9) | 81.9(10.2) | 81.4(9.8) | 81.6(9.4) |

10th Percentile (°/s) | 14.5(3.1) | 11.4(2.5) | 15.2(4.6) | 13.5(4.0) | 15.1(4.0) | 15.0(3.6) |

50th Percentile (°/s) | 86.0(10.6) | 57.6(7.6) | 78.5(9.9) | 82.6(10.8) | 82.7(10.4) | 83.5(9.9) |

90th Percentile (°/s) | 146.5(20.1) | 118.5(16.6) | 141.9(20.6) | 148.5(19.7) | 144.4(20.2) | 144.0(19.7) |

Percentile Range (90th – 10th)(°/s) | 131.9(20.2) | 107.1(16.2) | 126.7(19.7) | 135(18.9) | 129.3(19.9) | 128.9(19.8) |

Time at low velocities (<5°/s)(%) | 3.6(0.9) | 4.6(1.3) | 3.5(1.0) | 4.0(1.3) | 3.6(1.0) | 3.5(1.0) |

Time at high velocities (≥90/s)(%) | 46.7(6.1) | 24.1(6.9) | 41.3(7.6) | 44.9(6.1) | 44.6(6.5) | 45.3(6.1) |

Statistically-significant (p < 0.05) pair-wise tests between the Accel and the sensor fusion method.

Statistically-significant (p < 0.01) pair-wise tests between the Accel and the sensor fusion method.